Hybrid fractal zerotree wavelet image coding

n Orientatio l S a subband at the l th decomposition level and at one of three orientations D-R distortion-rate T 0 initial threshold c(i,j) the wavelet coefficient at location (i,j) x a function which chooses the largest integer less than x l D the domain tree whose coarsest coefficients are in the decomposition level l 1 − l R the range tree whose coarsest coefficients are in the decomposition level l-1 x the ordered set of coefficients of a range tree y the ordered set of coefficients of a subsampled domain tree isometry T the contractive transformation S subsampling O the orientation operation α the scaling factor a R the encoding bit rate b R a rate slightly less than the encoding rate f R the fractal coding rate n R the new rate) , (j i w k the coefficient of the coordinate (i,j) in the k th subband) , (ˆ j i w k the corresponding decoded coefficient k t the weighting value for the k th subband Abstract In this paper, a hybrid fractal zerotree wavelet (FZW) image coding algorithm is proposed. The algorithm couples a zerotree-based encoder, such as the embedded zerotree wavelet (EZW) coder or set partitioning in hierarchical trees, and a fractal image coder; this coupling is done in the wavelet domain. Based on perceptually-weighted distortion-rate calculations, a fractal method is adaptively applied to the parts of an image that can be encoded more efficiently relative to an EZW coder at a given rate. In addition to improving compression performance, the proposed algorithm also allows one to impose desirable properties from each type of image coder, such as progressive transmission, the zerotree structure, and range-domain block decoding. 4